A Fibonacci number series is like the example below,
1,1,2,3,5,8,13,21,34,55,89,144,233,377,610...... and so on
in general Fibonacci numbers are just the previous two numbers added together starting with 1 and 0 then goes on forever.
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1,1,2,3,5,8,13,21,34,55
A Fibonacci series
The ratio of successive terms in the Fibonacci sequence approaches the Golden ratio as the number of terms increases.
37 is not in the Fibonacci number series, but is the sum of two Fibonacci numbers, 34 and 3. Fibonacci numbers are with 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.
Yes - 5 is the fifth Fibonacci number.